Exploring the multi-dimensional structures and the detailed dynamics of a hadron has been one of the most primary goals in hadronic physics. In recent years, the so-called transverse momentum distributions (TMDs) associated with their evolutions, representing essential aspects of the partonic structures in momentum space (parton distributions not only as a function of longitudinal momentum fraction \(x\) , but also involves the intrinsic transverse momentum \(k_\perp \) ), have received a lot of concerns both in theory and experiment sides. A future planed deep inelastic scattering (DIS) facilities, such as electron-ion colliders (EIC) [1]}, [2]}, [3]}, LHeC [4]}, [5]} and EicC [6]}, will provide the cleanest environment to determine these fundamental quantities over a broad range of kinematics at high accuracy.
